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Operators usually have different notations (prefix, infix, postfix, ... ?), but expressions using them can all be transformed into expression trees.

E.g. ((a + b) * c) + 7

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Is this true for all expressions used in mathematics?

What insights can this give us?

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    @Unit No it's not - higher-arity operations just yield trees which split more than twice. (And even that can be gotten around via Currying.) – Noah Schweber Jul 06 '19 at 19:03

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